| Abstract: |
| In this talk we present explicit time-stepping schemes up to third-order accuracy for the shallow water equations, in which different time step sizes are used in different regions of the domain and are only restricted by respective local CFL conditions. The system is discretized in space by a C-grid staggering method, namely the TRiSK scheme (Ringler et al. 2010) adopted by MPAS-Ocean, a global ocean model with the capability of resolving multiple resolutions within a single simulation. The proposed local time-stepping schemes preserve all important properties of the spatial discretization, such as exact conservation of the mass and potential vorticity and conservation of the total energy within time-truncation errors. Numerical tests are presented to illustrate the performance of the proposed algorithms. |
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